A General Steepest Descent Algorithm

The following paper derives a general gradient process for extremization ion by imposing an " exponential decay" condition on the controlled variable. The general process is applied to two adaptive linear filter problems; a sonar application by Widrow [3] and a radar problem of Brennan & Reed [4]. The results are discussed in sections 11 and Ill, respectively. A central feature of the Fletcher-Powell process [1] is a matrix modification algorithm due to Davidon [2]. It is shown in Appendix A that this algorithm may be derived using the same exponential condition imposed on the proper error term.